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Punoxysm comments on A simple game that has no solution - Less Wrong Discussion
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Comments (123)
This can be analyzed as a regular 2-player game with payoff matrix
-- X Y
A 3,0 3,0
B 2,0 2,2
C 0,1 6,0
Player 2's indifference between X and Y when player 1 plays A means that player 2 only considers whether player 1 plays B or C.
Your model doesn't incorporate the uncertainty of my game. Even if Player 2 knows that Player 1 didn't play A, the fact that he could have impacts his estimate of whether Player 1 picked B or C.
I'm saying that Player 2's reward is strictly controlled by whatever fraction of the time player 1 plays B or C, since if player 1 plays A player 2's reward is guaranteed to be zero, and diminishes expected reward from X and Y in the same proportion.
If player 1 moves and when they pick either A,B or C player 2 is told "player 1 picked A, B or C" then player 2 can reduce it to only considering the possibility of B and C because even though A strictly dominates B, player 2's reward is only non-zero in the case where B or C are played.
This analysis would change if A,X were 3,0.5 or even 3,0.01
We look at game theory in different ways. By my analysis it is irrelevant what Player 2 would get if A were played, it could be $1 trillion or -$1 trillion and it would have no impact on the game as I see it. But then I don't use timeless decision theory, and you might be. This could be the source of our disagreement.
No, I'm just saying that since in your particular example Player 2 is indifferent when Player 1 chooses A, the fact that they don't get a decision doesn't matter. Nothing to do with TDT.